Numerical Investigation of a Refractive Index SPR D-Type Optical Fiber Sensor Using COMSOL Multiphysics

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1 Photonc Sensors (13) Vol. 3, No. 1: DOI: 1.17/s Regular Photonc Sensors Numercal Investgaton of a Refractve Index SPR D-Type Optcal Fber Sensor Usng COMSOL Multphyscs D. F. SANTOS 1,3, A. GUERREIRO,3, and J. M. BAPTISTA 1,3* 1 Centro de Cêncas Exatas e da Engenhara, Unversdade da Madera, Funchal, Portugal Faculdade de Cêncas da Unversdade do Porto, Portugal 3 INESC TEC, Porto, Portugal * Correspondng author: J. M. BAPTISTA E-mal: jmb@uma.pt Abstract: Recently, many programs have been developed for smulaton or analyss of the dfferent parameters of lght propagaton n optcal fbers, ether for sensng or for communcaton purposes. In ths paper, t s shown the COMSOL Multphyscs as a farly robust and smple program, due to the exstence of a graphcal envronment, to perform smulatons wth good accuracy. Results are compared wth other smulaton analyss, focusng on the surface plasmon resonance (SPR) phenomena for refractve ndex sensng n a D-type optcal fber, where the characterstcs of the materal layers, n terms of the type and thckness, and the resdual fber claddng thckness are optmzed. Keywords: Refractve ndex sensor, optcal fber sensor, surface plasmon resonance, lght propagaton smulaton, COMSOL Multphyscs, graphcal envronment Ctaton: D. F. SANTOS, A. GUERREIRO, and J. M. BAPTISTA, Numercal Investgaton of a Refractve Index SPR D-Type Optcal Fber Sensor Usng COMSOL Multphyscs, Photonc Sensors, vol. 3, no. 1, pp , Introducton To estmate the behavor of an optcal fber sensor, t s very mportant to use a smulaton tool to analyze parameters such as: magnetc and electrc feld ntenstes, effectve refractve ndex, among others. Several dffcultes exst n developng a good smulaton program, ncludng the necessary approxmatons when wrtng the code for D or 3D [1]. In partcular, when the sensor structure s complex, the calculaton becomes too cumbersome, and t s necessary to use smplfed methods, for example: expanson and propagaton method (MEP) and the method for multlayer structure transfer matrx modelng [ 3]. The latter allows a better approxmaton to the optcal fber cylndrcal structure [4], but fals to get good results for nano-structures n optcal fbers [1]. One soluton s to use fnte-dfference tme doman (FDTD), whch allows computng the magnetc and electrc feld dstrbuton, but requres huge quantty of computng memory [5]. In ths paper, we demonstrate another method of studyng the behavor of optcal fber sensors based on the surface plasmon resonance (SPR) usng COMSOL Multphyscs, a commercal program that uses fnte element method (FEM). On the other hand, D-type fber s an optcal fber wth numerous applcatons n optcal sensng for dfferent areas of engneerng. Gas detecton [6] and curvature sensng [7] are examples of sensng applcatons usng ths fber. The D-type fber has also been mplemented as a bosensor usng the surface-plasmon resonance technology [8, 9]. In ths Receved: 17 July 1 / Revsed verson: 31 July 1 The Author(s) 1. Ths artcle s publshed wth open access at Sprngerlnk.com

2 6 Photonc Sensors smulaton work, we mproved the desgn of an SPR refractve ndex sensor, based on a D-type optcal fber, where the characterstcs of the materal layers, n terms of type and thckness, and the resdual fber claddng thckness were optmzed.. Theory We have analyzed an optcal fber sensor based on SPR composed by a D-type fber splced between two sngle mode fbers, as shown n Fg. 1. The man desgn parameters of the sensor ncluded the length of the sensor L, the radus and refractve ndex of the core (r c and n c, respectvely) and of the claddng (r cladd and n cladd, respectvely), the dstance between the core and the metal d (the resdual claddng), the thckness of the metal d m, and the refractve ndex of the external medum n ext. n cladd n c n ext n m L d m d r c r cladd Fg. 1 Typcal structure and behavor of a D-type fber optc sensor based on SPR. The losses of the lght propagatng n the fber were determned by the tunng between the wavelength of the lght beam and the SPR whch was strongly dependent on the refractve ndex of the external medum. The transmsson coeffcent of the sensor could be used to assess wth accuracy the value of n ext..1 Calculated transmsson coeffcent usng COMSOL In ths work, we have conducted a D analyss of the mode structure and the electromagnetc feld modes along the transverse plane of a D-type fber usng the mode analyss utltes of COMSOL Multphyscs. The electromagnetc felds n optcal fber wavegudes are governed by the macroscopc Maxwell s equatons n the absence of currents or external electrc charges: (,) rt E (,) rt B (1) dt (,) rt H(,) rt J (,) rt D () dt D (,) rt B (,) rt (3) (,) rt (4) where E, H, D and B are the electrc, the magnetc, the delectrc and the magnetc nducton felds, respectvely. Also, the term J s the current densty, s the charge densty, r s the spatal coordnate, and t denotes tme. The tme-harmonc solutons descrbng strctly monochromatc felds are of the form E(,) rt E (, r) (5) H(,) rt H (, r) (6) where s the angular frequency of lght. In ths representaton, the felds are complex quanttes whose real parts correspond to the physcal felds [1]. In lnear, sotropc, and nonmagnetc meda, the followng consttutve relatons are D(,) rt re (, r) (7) B(,) rt H (, r) (8) where and are the permttvty and permeablty of free space, respectvely, and r denotes the relatve, materal-dependent permttvty. In general, these quanttes are functons of the spatal coordnates. Takng the curl of (1) and usng (3), (7) and (8) yelds the wave equaton for the Fourer components electrc feld [1]: ( E( r, ) k [ r ( r, )] E( r, ). (9) the same s the magnetc feld: 1 [ r ( r, )] H( r, ) k H( r, ) (1) where c s the speed of lght, and 1 k c s the wave number of the mode of the feld. The term r(, r ) r(, r ) j(, r )/ represents the complex relatve delectrc functon wrtten n terms of the materal-dependent (real valued) relatve permttvty r and the Ohmc conductvty of the materal (, r ). In optcal fbers, the dependency n the spatal z coordnate along the axs s obtaned usng the varable separaton method:

3 D. F. SANTOS et al.: Numercal Investgaton of a Refractve Index SPR D-Type Optcal Fber Sensor Usng COMSOL Multphyscs 63 j z E (, r ) E ( r, ) (11) j z H (, r ) H ( r, ) (1) where s the propagaton constant of the -th mode, and r s the poston vector n the plane perpendcular to the optcal axs. The solutons of (9) and (1) were obtaned usng the FEM, whch bascally conssts n dvdng the smulaton doman nto smaller subdomans formng a mesh as shown n Fg.. The subdomans have dfferent szes and are smaller near the nterfaces between dfferent meda to account for steeper varatons of the feld. The feld equatons are then dscretzed nto an algebrac system of equatons and solved for ther characterstc egenvalues. nm( ) jkm( ) m( ) (15) where n m and k m are the real and magnary values of the refractve ndex for the metal, respectvely, m s the permttvty complex metal, and λ c and λ p denote the plasma wavelength and the collson wavelength, respectvely, that s defned n [3] for the metals Ag, Au, Cu and Al. Fgure 3 llustrates the ntensty of the electrc feld usng the study Mode Analyses from COMSOL Multphyscs, for the structure of Fg. 1 and the mesh of Fg. wth [Fg. 3(a)] and wthout [Fg. 3(b)] a metallc layer, n ths case of a 65-nm-thckness gold layer. The wavelength of the lght was 8 nm. The study allowed confrmng the sngle-mode behavor propagaton n the optcal fber. Fg. Structure of the fnte elements n COMSOL Multphyscs for a D-type optcal fber wth a metallc layer for SPR. The electrc and magnetc felds are dependent on the angular frequency [(9) and (1)] as well as on the refractve ndex of the materals. For that, t s necessary to calculate the materal s refractve ndex for all frequences under study. For a delectrc layer, n ths case of an optcal fber, t s possble to use the Sellmeer equaton [3] 3 B q n ( ) 1 (13) q1 Cq where B q, C q are the Sellmeer coeffcents, determned expermentally [11], for a germanum-doped slca core fber and fluorne-doped slca claddng. For the metallc layer, the permttvty and the refractve ndex can be obtaned from the Drude model as c p c j m ( ) 1 ( ) (14) (a) (b) Fg. 3 Electrc feld dstrbuton D near the fber core for =8 nm (a) wth the metal (Au) wth a thckness of 65 nm and (b) wthout the metal.

4 64 Photonc Sensors The 1D electrcal feld ampltude n the optcal fber s also shown n Fgs. 4(a) and 4(b), wth and wthout a metallc layer, respectvely. Comparng both fgures, t s possble to see the electrc feld ntensty external to the fber s stronger when usng the metal. Electrc feld ampltude (V/m) Electrc feld ampltude (V/m) Arc length (a) Arc length (b) Fg. 4 Electrc feld ampltude 1D across the fber core for =8 nm (a) wth the metal (Au) wth a thckness of 65 nm and (b) wthout the metal. Based on the smulaton results provded by the COMSOL Multphyscs, one can compute the effectve refractve ndex n eff of the sensor [5] and from t the transmsson coeffcent T as a functon of the wavelength, the external refractve ndex n ext and the thckness of the metal d m, accordng to the expresson neff (, next, d) kl T(, n, d ) e. (16) ext m. Transmsson coeffcent calculated usng Fresnel laws To verfy that the method works properly, a comparson was made wth the mplemented algorthm n [1], whch used Fresnel equatons appled to the structure n Fg. 1, allowng the transmsson ntensty to be wrtten (for four layers) as L/ rc tan T(, next, d) ( r134) (17) where r 134 s the reflectve coeffcent for four layers as wrtten j kd r1 r34e r134 (18) j kd 1 rr 1 34e where the reflectve coeffcents for three layers and two layers are, respectvely j kd 3 r3 r34 e r34 (19) j kd 3 1 r3r34e n / k nj / kj rj () n / k n / k j j where k s the component of the wave vector of the nterface of the two layers of the sensor n the 1/ drecton z and s gven as k k( n n1sn ), where n 1, n, n 3 and n 4 represent the refractve ndces of the core, claddng, metal and the external test medum, respectvely. Applyng (16) and (17), t s possble to obtan the results by the two dfferent methods, as shown n Fg. 5. The behavor of the two methods was smlar, havng a dfference between the transmsson coeffcents and a small shft n the wavelength dps. We attrbuted ths dfference to the fact that n the Fresnel equatons algorthm t s only consdered planar waves n a farly symmetrcal arrangement. On the other hand, when usng the FEM, we consdered the D-type fber as a non-symmetrcal cylndrcal wavegude, beng able to model the nhomogeneous optcal regons wth a resoluton of the cell sze, resultng n a more accurate outcome. In terms of the results and n what concerns the materal thckness, the optmal pont occurred when a layer wth a thckness of 55 nm to 65 nm was used.

5 D. F. SANTOS et al.: Numercal Investgaton of a Refractve Index SPR D-Type Optcal Fber Sensor Usng COMSOL Multphyscs 65 Another way to test the effcency of the descrbed procedure s to calculate the sensor senstvty (/RIU) as functon of the dfferent refractve ndces of the external envronment. The senstvty for both methods s almost equal and s close to 315 nm/riu []. Talorng the smulaton analyss n COMSOL Multphyscs, t s possble to optmze the senstvty, transmsson coeffcent dp, wavelength operaton area, amongst others for a refractve ndex SPR D-type optcal fber sensor. To decrease the depth of the transmsson coeffcent dp and consequently lower the senstvty of the external medum, d can be ncreased, as shown n Fg. 6. Transmsson coeffcent Thckness of gold, 45 (nm)_comsol Thckness of gold, 55 (nm)_comsol Thckness of gold, 65 (nm)_comsol Thckness of gold, 75 (nm)_comsol Thckness of gold, 45 (n m)_teorco Thckness of gold, 55 (n m)_teorco Thckness of gold, 65 (n m)_teorco Thckness of gold, 75 (n m)_teorco Waveleng th (μ m) Fg. 5 Transmsson coeffcent T as a functon of the wavelength and metallc layer thcknesses (Au), d m = m, L= 1 mm, n ext = and = From Fgs. 5 and 6, t s possble to have a sensor that works for an area of operaton near 8 nm, for a metal thckness of 65 nm (Au). In case another wavelength s requred, one possble soluton s to apply an addtonal layer of a delectrc wth a hgh refractve ndex, such as tantalum pentoxde (Ta O 5 )[1 ], whch smulaton results can be seen n Fg. 7 and compared wth the results presented n []. For dfferent thcknesses of Ta O 5, the transmsson coeffcent dp of the sensor operaton s not sgnfcantly altered beng possble to talor the wavelength sensor operaton []. Transmsson coeffcent d= μm d=.5 μm d=1. μm d=. μm Wavelength (μm) Fg. 6 Smulaton of transmsson coeffcent of the sensor, for dfferent claddng thcknesses: n ths smulaton, the thckness of the gold layer s 65 nm, and the refractve ndex of the external envronment s Transmsson coeffcent Wavelength (μm) T hckness of TAO, nm T hckness of TAO, 5 nm T hckness of TAO, 3 nm Fg. 7 Smulaton of transmsson coeffcent T of the sensor for dfferent thcknesses of the delectrc (Ta O 5 ): the thckness of the gold s 65 nm and n ext = Conclusons Another method was demonstrated to study the behavor of optcal fber sensors for refractve ndex measurement based on SPR usng COMSOL Multphyscs, a commercal program that uses the fnte element method. The two smulatons, one wth COMSOL Multphyscs and the other wth Fresnel s equatons, present a smlar behavor. The graphcal nterface of COMSOL Multphyscs facltates the smulaton work, havng no need to

6 66 Photonc Sensors develop complex formulatons. Also, t has the ablty to model nhomogeneous optcal regons wth a resoluton of the cell sze and allows the analyss of other parameters such as the ntensty of magnetc and electrc feld across the structure [13]. COMSOL Multphyscs permts n a graphcal envronment more accurate and realstc results than tradtonal approaches, although at the expense of longer runnng tme. It was also possble to demonstrate the use of COMSOL Multphyscs to mprove the performance of a refractve ndex SPR D-type optcal fber sensor, where the characterstcs of the materal layers, n terms of the type and thckness, and the resdual fber claddng thckness are optmzed. Open Access Ths artcle s dstrbuted under the terms of the Creatve Commons Attrbuton Lcense whch permts any use, dstrbuton, and reproducton n any medum, provded the orgnal author(s) and source are credted. References [1] B. Lee, S. Roh, and J. Park, Current status of mcroand nano-structured optcal fber sensors, Optcal Fber Technology, vol. 15, no. 3, pp. 9 1, 9. [] R. Slavk, J. Homola, J. Ctyroký, and E. Brynda, Novel spectral fber optc sensor based on surface plasmon resonance, Sensors and Actuators B: Chemcal, vol. 74, no. 1 4, pp , 1. [3] A. K. Sharma and B. D. Gupta, On the performance of dfferent bmetallc combnatons n surface plasmon resonance based fber optc sensors, Journal of Appled Physcs, vol. 11, no. 9, p , 7. [4] E. Anemoganns, E. N. Glytss, and T. K. Gaylord, Transmsson characterstcs of long-perod fber gratngs havng arbtrary azmuthal/radal refractve ndex varatons, Journal of Lghtwave Technology, vol. 1, no. 1, pp. 18 7, 3. [5] Y. Al-Qazwn, P. T. Arasu, and A. S. M. Noor, Numercal nvestgaton of the performance of an SPR-based optcal fber sensor n an aqueous envronment usng fnte-dfference tme doman, n Proc. 11 nd Internatonal Conference on Photoncs, Oct , vol. 1, pp. 1 4, 11. [6] B. Culshaw, F. Muhammad, R. Van Ewyk, G. Stewart, S. Murray, D. Pnchbeck, et al., Evanescent wave methane detecton usng optcal fbers, Electroncs Letters, vol. 8, no. 4, pp. 3 34, 199. [7] F. M. Araújo, L. A. Ferrera, J. L. Santos, and F. Farah, Temperature and stran nsenstve bendng measurements wth D-type fber Bragg gratngs, Measurement Scence and Technology, vol. 1, no. 7, pp , 1. [8] M. H. Chu, S. F. Wang, and R. S. Chang, D-type fber bosensor based on surface-plasmon resonance technology and heterodyne nterferometry, Optcs Letters, vol. 3, no. 3, pp , 5. [9] Y. Chen and H. Mng, Revew of surface plasmon resonance and localzed surface plasmon resonance sensor, Photoncs Sensors, vol., no. 1, pp , 1. [1] M. Flzan and F. Marade, Edge element analyss of complex confguratons n presence of shelds, IEEE Transactons on Magnetcs, vol. 33, no., pp , [11] A. Méndez and T. F. Morse, Specalty Optcal Fbers Handbook. San Dego, Calforna: Academc Press, 7, pp [1] M. H. Chu, C. H. Shh, and M. H. Ch, Optmum senstvty of sngle-mode D-type optcal fber sensor n the ntensty measurement, Sensors and Actuators B: Chemcal, vol. 13, no., pp , 7. [13] D. Chrstensen and D. Fowers, Modelng SPR sensors wth the fnte-dfference tme-doman method, Bosensors & Boelectroncs, vol. 11, no. 6, pp , 1996.